Based on what you are saying, I think you are OK and it's normal. The guage strings you have on your guitars is fine. Due to the scale length difference between a strat and a lp, 10's on a lp have about the same tension as 9's on a strat. I happen to put 10's on my strat because the heavier guage strings hold up to my sweaty hands much better.

A few months ago, I was working on a bunch of songs that were all barre chords. At first, my hands started to cramp. After a few weeks, I built up endurance that that went away. Another time, I was working on a phrase in a solo that had a lot of bends. After about 2 hours of that, my finger tips were killing me. It went away after a day or two.

I'd be interested to hear what others' experience is...perhaps we are both wierd :-).